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# If x and y are integers and xy = 6, what is the value of x?

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If x and y are integers and xy = 6, what is the value of x?  [#permalink]

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28 Oct 2019, 09:07
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85% (hard)

Question Stats:

43% (01:55) correct 57% (01:30) wrong based on 95 sessions

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If x and y are integers and xy = 6, what is the value of x?

(1) x > y + 1
(2) x = 6y

Chetan's questions

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Re: If x and y are integers and xy = 6, what is the value of x?  [#permalink]

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28 Oct 2019, 09:55
2
Will go with C
1. x> 6/x + 1. Simplify !
---> [(x-3)(x+2)]/x > 0 so the range is x is between -2 and 0 i.e. x = -1 or x = more than 3 i.e. x= 6 . Not sufficient

2. x^2 = 36 ----> x = 6 or -6 . Insufficient

Combining 1 and 2 ---> unique x is 6.
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Re: If x and y are integers and xy = 6, what is the value of x?  [#permalink]

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28 Oct 2019, 14:59
chetan2u wrote:
If x and y are integers and xy = 6, what is the value of x?

(1) x > y + 1
(2) x = 6y

Chetan's questions

Since x and y are integers, they can take the values of (2,3),(6,1),(-2,-3),(-6,-1) for xy = 6.

Statement 1, x > y + 1. x can be either -1 or 6. NOT SUFFICIENT.

Statement 2, x = 6y. x can be 6 or -6. NOT SUFFICIENT.

Combining both statement, 6 is the single value that meets the requirements. SUFFICIENT.

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Re: If x and y are integers and xy = 6, what is the value of x?  [#permalink]

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29 Oct 2019, 02:10
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I think its C.

1- (x,y) = (-1,-6) / (6,1)
2- (x,y) = (-6,-1) / (6,1)

Therefore x=6.
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Re: If x and y are integers and xy = 6, what is the value of x?  [#permalink]

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19 Nov 2019, 05:45
chetan2u wrote:
If x and y are integers and xy = 6, what is the value of x?

(1) x > y + 1
(2) x = 6y

(x,y)=integers: xy=6, (x,y;y,x)=(2,3;-2,-3;6,1;-1,-6)

(1) x > y + 1 insufic
(x,y)=(6,1;-1,-6); x=(6,-1)

(2) x = 6y insufic
(x,y)=(6,1;-6,-1); x=(6,-6)

(1&2) sufic
x=6

Ans (C)
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Re: If x and y are integers and xy = 6, what is the value of x?  [#permalink]

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20 Nov 2019, 23:44
chetan2u wrote:
If x and y are integers and xy = 6, what is the value of x?

(1) x > y + 1
(2) x = 6y

Chetan's questions

Note : no sign specific.

xy = 6

1*6 = 6
2*3 = 6

the values could be negative too.

we are looking for the value of x.

Statement 1; x>y + 1

x - y > 1

It indicates that both x and y are positive.

but it's not possible to separate the value of x.

Statement 2;

x = 6y

Given ,

xy = 6

6y*y = 6

$$y^2 = 1$$

y = +1 or - 1.

Thus , NOT sufficient.

Combining both statements :

From statement 1, we know that both x and y are positive and from 2nd statement we know that y must be 1.

xy = 6

x(1) = 6

x = 6 .

C is the correct statement .
Re: If x and y are integers and xy = 6, what is the value of x?   [#permalink] 20 Nov 2019, 23:44
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